Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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This invention refers to an improved chain bar for a power chain
saw apparatus, which is useful for preventing the occupational
hazard, commonly referred to as vibration white finger, a
problem common to power chain saw operators, especially in cold,
damp climates.
BACKGROUND OF THE INVENTION
Both full-time tree fallers and casual domestic wood gatherers
use power chain saws that subject their hands to a spectrum of
resonant harmonic vibrations at the hand grips, which cause a
circulatory ailment, known as vibration white finger, in the
fingers due to prolonged gripping in cold, damp climates, with
excessive vibration levels transferred to the hands.Initially,
a temporary numbness progresses into tingling in the fingers
as they slowly turn white, and, as the condition progresses,
permanent numbness and7in rare cases, gangrene can develop.
The methods and apparatus Eor -the prevention of this occupational
hazard to power chain saw operators must become more sophistica-ted
to meet the changing international standards in occupational
safety and health, as in Sweden, where the most rigid govermnent
regulations concerning power chain saws are enforced.
Reference (1) indicates that there appears to be an incubation
period of up to 1 year for vibration-susceptible power chain saw
operators, and up to 5 years for vibration-resistant power chain
saw operators, before vibration white finger develops into an
occupational hazard.
This invention relates to an improved chain saw bar for a power
chain saw apparatus -that is a further development of the resonant
chain bar analysis by Leith (2) in which five separate famil:ies
of resonant harmonic vibration sources are recognized as
available for transmission to the hand grips, and hence to the
operators' tingers~
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a) the chain bar which vibrates as a cantilever beam with
combined longitudinal tension/compression and transverse/
lateral bending resonant vibrations,
b) resonant wood sawing slot/tree vibration acting as a
Helmholtz resonator,
c) power chain saw crankshaft rotation rpm,
d) intake manifold vibrations acting as a Helmholtz resonator
at twice the crankshaft rotation rpm, and
e) the chain assembly as a vibrating string.
PRIOR ART
Swallow (4) in British pa-tent 513171 introduced the concep-t of
reducing panel vibrations by a constrained layer damper. Ross
et al (5), in 1959, described the damping of plate flexural
vibrations by means of a shear motion of viscoelastic laminae.
The Third International Symposium on Hand-Arm Vibrations (1) held
in 1981, summarized the many speculations and sparse facts on the
complex nature of vibration white finger, which seems to be a more
prevalent occupational hazard in Canada, Europe, and Japan than is
reported in the USA. It is well-known to professional tree-fallers,
that there are two conflicting resonant conditions in the applicable
range of 100 to 400 Hertz that are to be considered in industrial
chain saw operation:
a? minimum operating cost which requires a resonant wood sawing
mode with the maximum energy efficiency at the tree end of the
bar/chain/tree interface, and
b) prevention of vibration white finger, which would invalve
some method to damp ou-t at least a portion of the combined
longitudinal tension/compression and transverse/lateral
bending resonant vlbrations in the range of 100 to 400 ~ertæ
golng to the ~lxed end oE the bar/chaln/hand grlp :inteIface,
and hence to the fallers' fingers.
~2~ J
Miles (3) in USA patent 4425980 mentions beam dampers for damping
the vibrations of the skin of reinforced structures,which is a
recent reference on damping in general, but does not men-tion
chain bars. Obviously, there is a great need to develop an
improved chain bar for both full-time tree fallers and casual
domestic wood gatherers, since the Third International Symposium
on Hand Arm Vibrations held in Ottawa in 1981 (1), estimates that
one-third of Canada's 26,000 tree fallers exhibit some degree of
vibration white finger related to the cold, damp climate; and it
appears probable that a lesser problem may be undetected in the
Uni-ted States' 300,000 tree fallers, related to the milder, damp
climate.
Leith (2) in Canada patent 1173330 describes a "critica] damped"
laminated chain bar, but utilizes only the transverse bending
vibration analysis.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide an improved
chain bar for a power chain saw apparatus, which consists of a
; replaceable chain bar with one or more thru-slots or holes that
are fitted with a damping insert. The improved chain bar retains
the maximum energy efficiency for wood sawing, but damps out up to
95 % of the combined longitudinal tension/compression and the
transverse/lateral bending vibrations going to the hand grips,
and hence to the operators' hands. Thus, the reduced vibration
energy at the hand grips prolongs the incubation period before
vibration white finger symptoms become an obvious ha~ard.
Accordingly, there is provided a chain bar for a power chain saw
apparatus, including a gasoline/diesel engine, hand grips, a
crankshaft-mounted drive sprocket,a replaceable chain bar having
a longitudinal axis and having a fixed end a-ttached to the engine,
a continuous loop of chain having cutter teeth sliding around the
chain bar, a drive sprocket, and a guide sprocket, said chain saw,
when operated, having in said chain bar vibrations which, when
expressed in vibration harmonic frequensy curves, have at least
one area of maximum deflection, charac-terized in that said chain
iO bar is provided with at least one thru-slot, said thru-slot is
positioned along said longitudinal axis of said chain bar between
and spaced away from said fixed end and said guide sprocket, said
thru-slot is located in said at least one area of maximum
deflection of the harmonics of each of the vibrations in said
chain bar in relation to the dimensions of said chain bar; each
: said thru-slot is fitted with a damping insert, said damping
insert being made of at least one damping material; such that
chain bar is substantially non-resonant, whereby up to 95% of
the combined longitudinal tension/compression and transverse/
la-teral bending vibration energy going to said hand grips is
absorbed. Preferably, said thru-slot has one of a number of
shapes, including a square, retangular, triangular, oval,
polygon, circular, and the like shapes, the surface area of
which is expressed as the diameter of a substantially circular
shape of equivalent surface area, said diameter being in the
range of about one quarter to one half of the width of the
chain bar. Preferably,said thru-slot has a slot perimeter edge
profile, said damping insert has an insert perimeter edge
profile, and said slot profile and said insert profi.le are in
face-to-face matching contact.
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BRIEF DESCRIPTION OF DRAWINGS ~ i
The embodiments of the invention will now be described with
reference to the accompanyi.ng drawings of which Figure 1 is a
diagrammatic side view, partly in section, of the power chain
saw apparatus, sawing a log/tree;
Figure 2 is a detailed side view of the chain saw cutter teeth,
saw-cut notch and -the log/tree;
Figure 3 is a diagrammatic side view of the chain bar, with
directions indicated for the longitudinal, transverse and
lateral vibrations;
Figure 4 is a cross section through line I-I in Figure 3
showing one preferred embodiment of a thru-slot fitted with
a damping insert; and
Figure 5 is a cross section through line I-l in Figure 3
showing an alternative embodiment of the thru-slot fi-tted
with a damping insert.
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DETAILED DESCRIPTIONS
Referring first to Figure l, a power chain saw apparatus includes
a gasoline or diesel engine 1, with hand-grip mounts 2, with a
crankshaft-mounted drive sprocke-t 3, having a continuous loop of
chain 4 sliding along the sides of a replaceable sword-shaped
chain bar 5 having a fixed end attached to the engine 1, and
around an outboard guide sprocket 6. The chain 4 has
multiplicities of separate connecting links 7 and cutter teeth 8.
The chain bar 5 can vibrate in any combination of three separate
or comhined harmonic vibration modes, that is, as shown in
Figure 3, along the longitudinal axis A, the transverse axis B,
or the lateral axis C. As shown in Figure 2, the cutter teeth 8
cut out a saw~cut notch 10 in the tree/log 9, which cut is wide
enough for the chain bar assembly to slide with clearance through
the saw-cut notch 10.
The chain cutter teeth 8 initiate a maximum energy efficiency
sawing mode by exciting the uncut wood section of the tree/log
to respond as a Helmholtz resonator, see reference (2).
Figure 3 shows a side view of chain bar 5 according to the invention.
Chain bar 5 has a mounting slot 12 with which it is attached to
engine 1. Chain bar 5 has at least one hole or thru-slot 13 in
the main body 14 of chain bar 5. Thru-slot 13 may have one of a
number of shapes including but not limited to a square, rectang-llar,
triangular, oval, polygon, circular, or the like shape. The
preferred shape of the thru-slot 13 as shown in Figure 3 is a
substan-tially circular shape. Thru-slot 13 may be made by
machining, drilling, plmching, or like operations known in the
art .
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~Thru-slot 13 is preferably located substantially along the I I
longitudinal axis A of the chain bar 5 between guide sprocket 6
and mounting slot 12 and spaced away therefrom. The size,
location and number of thru-slot 13 may vary dependent on the
dimensions of chain bar 5, the amount of damping of vibrations
that is required, and the harmonicsof the vibrations in the
chain bar 5. The size of a thru-slot is conveniently expressed
as the diame-ter of a slot of circular shape, the size of
differently shaped slots being such that the surface area of
]0 such slots is substantially equivalent to that of a circular
slot with the given diameter. The diameter of a thru-slot 13
is generally in the range of about one quarter to one half of the
width of a chain bar 5. Accordingly, depending on the dimensions
of the chain bar 5, the diameter of thru-slots 13 is in the
range of about 0.5 to 2 inch (1.2 to 5.1 cm). For those chain
bars that require more than one thru-slot in the chain bar to
damp out the vibrations to the required degree, the thru-slots
13 may have either different diameters or substantially the same
diameters. The location and number of thru-slots 13 is
dependent on the harmonics and sub-harmonics of the
longitudinal, transverse, and lateral vibrations of the chain
bar as will be explained. The number of thru-slots 13 is
generally in the range of one to ten.
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Each thru-slot 13 has a slot perimeter edge profile, the edge
has a surface. The slot perimeter edge pro~ile is conveniently
machined at the perimeter of the slot. The proEile may have a
variety of shapes but the number of shapes is limited for
practical reasons to those shapes that are easily machined~
Suitable and preferred profiles are those having a generally
V-shape or U-shape, -the legs of the V or U being pointed either
inwards or outwards towards the centre of chain bar 5. Slot
perimeter edge profiles of generally V-shaped cross section are
illustrated in Figures 4 and 5, wherein 16 indicates a slot
perimeter edge profile having a generally V-shaped profile
pointing inwards and 17 indicates a profile having a generally
V-shaped profile pointing outwards, respectively.
The surface of the slot perimeter edge profile of thru-slot 13
perferably has an embossed surface such as with multiple ridges,
perforations, grooves, or dimples to provide more surface area
for the resilient fit between the thru-slot 13 and a tlamping
insert 15. Each thru-slot 13 contains a damping insert 15 which
is fitted, bonded, crimped, cast, or moulded in slot 13.
The insert 15 together with the chain bar 5 utili~es -the two
different Young's moduli of elasticity as the basis of
structural damping. The damping insert 15 may be made of any
one or more of a number o-f suitable materials that, in
combination with the (usually steel~ chain bar, provides
damping of vibrations. Suitable damping materials antl the
transmissibility of each material for structural damping are
shown in Table I.
TABLE I
TRANSMISSIBILITY * OF MATERIALS AS COMPARED TO STEEL
carbon 9% gallium 4%
gold 19% indium 6%
lead 5% zinc 73%
thallium3% silver 26%
tin 26% nylon 15%
hard rubber-ebonite 11%
polyester resin 6%
polyester and chopped s-trand 25%
polyester and glass clo-th 36%
polye-thy~ene 1%
rigid polyvi.nylchloride 10%
birch 36%
* Transmissibility % = 2
(Vs) _ 1
: (Vm)2
wherein Vs = wave velocity in steel
Vm = wave velocity in specified material
The choic~ of damping material depends on the damping of vibratio1s
that is required. For example, when 90% damping is required, the
choice of damping material is restricted to those materials that
have a transmissibility of 10% or less, and when 50% damping is
required, the transmissibility of the damping material should be
50% or less. Damping in % is defined as 100% minus
transmissibility in %.
Particularly suitable materials are those that have a low
transmissibility, especially those with less than 40%
transmissibility. In the case wherein the chain bar has more
than one thru-slot, the damping inserts may be made of the same
or of different materials. Each damping insert may be composed
of more than one of the sui table damping materials listed in
Table I, such as, two or more damping materials. For example,
a mixture of metal or wood and polyester resin may be used,
the metal or wood being in the form of fibres or chips.
Such mixture is hereby defined as including composites and
laminates, such as, for example,a composite or laminate of one
o the named plastic materials with wood, metal or carbon.
The damping insert 15 has an insert perimeter edge profile,
which is the negative or inverse of the slo-t perimeter edge
profile. In Figures 4 and 5, the slot perimeter profiles are
indicated at 16 and 17, and the insert perimeter edge profile
at 18 and 19, respectively. The insert perimeter profile is
in face-to-face matching contact with the slot perimeter
profile. The thickness of the chain bar 5 with the damping
insert 15 in each thru-slot 13 is less than the width of the
cutter teeth 8 on the chain. A chain bar with the at least one
thru-slot fitted with a damping insert is substantailly non--
resonant whereby up to 95% oE the combined longitudinal
tension/cornpression and transverse/lateral bending energy
going to the hand grlps is absorbed.
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The thru-slot 13 or thru-slots with damping insert is located,
as stated above, essentially on the longitudinal axis A of
chain bar 5 between mounting slot 12 and guide sprocke-t 6 ~ut
spaced away therefrom. Two or more 910ts are located in spaced
relation. The thru-slot(s) is/are ]ocated generally in -the
area~s) of maximum deflection(s) for each harmonic of a
vibration. Depending on the shape of the vibration frequency
curve, more than one thru-slot may be located in an area oE
maximum deflection. The exact location and the number-of
thru-slots with damping insert is determined with reference
to Tables II, III and IV.
TABLE II
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STEEL CHAIN BAR CHAIN SAW
a b c d
Length ~ (inch) 16 30 45 60
(cm) 38 76 114 152
Width w (inch) 2.4 3.1 3.53.75
(cm) 6 8 9 9.5
Thickness~ (inch) 0.18 0.2 0.22 0.25
(cm) ¦ 0.46 0.51 0.56 0.64
TABLE III
RESONANT HARMONIC VIBRATIONS OF THE CIIAIN BARS
Chain saw _ _ a b c __ _d
Transverse Harmonics~' f= _ ~ = An (9462) _
2n ~u ~ ~2
An = 3.52 n=l ~ 88 39 22
An = 22 n=2 1931 550
An = 61.7 n=3 5416 1543 684
Longitudinal Suh-Harmonics~'- f = N 2 ~ = 51489 Ns
2 u ~2
Ns =0 3218 1716 1144 858
Ns = 2 1609 858572 429
Ns = 1/3 1073 572
Ns = 4 805 429
_ ___.__ _ _ _
Lateral Harmonics~ f = An ~ = An (9462) t
2n u ~4
An = 3.52 n = 1 23.4 7.4 3.6 2.3
An = 22 n = 2 ~ 46 22.6 14.5
An = 61.7 n = 3 410 ~ 63.3 40.5
An = 200 n =4 1330 418
An = 300 n =5 1994 627
; ~' see reference 7 ~ = length w = width t = thickness
An = constant for cantilever beam bending
N = constant for axial tension and compression
n = number of wave length
Ns - number of sub-harmonic wave length
f = Erequency E = Young's modulus of elasticity
I = sect:ion modulus A = beam cross sect:Lon area
u = mass dens:lty
~25;~4~3
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TABLE IV
RESONANT FREQUENCIES AT VARIOUS TRANSMISSIBILITY/DAMPING VALUES
Transmissibility % 10 25 50 75 100
damping % 90 75 50 25 undamped
; Chain Bar Resonant Frequencies in Hertz
120 179 231 262 400
106 157 202 229 350
91 134 173 197 300
112 144 164 250
89 116 131 200
67 87 98 150
58 66 100
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By way of examples, four chain saws a, b, c, and d are identified
in Table II by the length Q, width w and thickness t of the chain
bar.
Table III defines the resonant harmonic vibrations comprising the
transverse harmonic, the longitudinal sub-harmonic and the lateral
harmonic frequencies for the chain bar of chain saws a, b, c, and
d as calculated using the formulas given by den Hartog (7).
Table IV shows the resonant frequencies at various transmissibility/
damping values and defines what damping in æ is required to reduce
the resonant frequencies of the chain bar, which without damping
are in the range of about 100 to 400 Hertz (column 5), to about
100 Hertz or less. Damping in % is defined as 100% minus
transmissibility in ~,. The degree of damping required,as dictated
by the desired frequency of vibration9defines the transmissibility
necessary to attain that degree of damping and hence determines
the materLa1 for the damping insert . The appropr:iate damping
~material can then be selected from materials listed in Table I.
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~rom Table III follows that, for chain saw a, chain bar resonant
frequencies in the 100 to 400 Hertz range are 309 Hertz for n = 1
of the transverse harmonics and 146 Hertz for n = 2 of the lateral
harmonics. In order to reduce the undamped transverse harmonic
frequency of 309 Hertz to less than 100 Hertz, 90% damping is
required (Table IV shows that at 300 Hertz, the improved chain
bar frequency is 91 Hertz). This 90~ damping is attained by
providing one thru-slot with insert in the area of maximum
deflection which is 5 inch (13 cm) from sprocket 6 for n = 1 of
- 10 the transverse harmonic vibrations. The thru-slot diameter is
chosen at half -the bar width or 1.25 inch (3 cm). In order to
reduce the undamped lateral harmonic frequency of 146 Hertz to
less than 100 Hertz, at least 25% damping is required. Because
the damping is not entirely provided by the first thru-slot, the
use of a second slot is indicated. Hence a second slo-t with insert
with a diameter of 1 inch (2.5 cm) is provided in the area of
maximum deflection of the lateral harmonic vibrations for n = 2
which is at 10 inch (25 cm~ from sprocket 6.
Similarly for chain saw b, it follows from Table III that the only
chain bar resonant frequency in the 100 to 400 Hertz range is at
129 Hertz for n = 3 of the lateral harmonics. To reduce this
undamped frequency to 100 hertz or less it follows from Table IV
that at least 25% damping is required ( at 150 Hertz the 25%
damped chain bar frequency is 98 Hertz, while 50% damping reduces
the frequency to 87 Hertz). 25% damping of the n = 3 1ateral
harmonics is attained by providing three thru-slots, each having
a diameter chosen at 1 inch (2.5 cm) and fit-ted with a damping
insert. ~ach slot with insert is positioned at each of the three
areas of maximum deflection oE the lateral harmonic vibrations,
whlch are at d:istances of 6, 15, an(] 25 inch (15, 38, and 61 cm),
resp~ctively, from guide sproclcet 6.
For chain saw c, it follows from Table III that the chain bar
resonant frequencies in the 100 to 400 Hertz range are at 244
Hertz for n = 2 transverse harmonics; at 381 llertz for Ns = 1/3
and at 286 Hertz for Ns = 4 of the longitudinal harmonics; and at
206 Hertz for n = 4 and at 309 Hertz for n = 5 of the lateral
harmonics. It follows from Table IV that a reduction to 100 Hertz
or less of these undamped frequencies requires 90~ damping.
90~ damping of the harmonics and sub-harmonics of the vibrations
are attained by providing five thru-slots of 2 inch (5 cm) diameter,
each with damping inser-ts at each oE the five areas of maximum
deflection of the frequency curves. The frequency curves
corresponding to each of the harmonics n = 2, 4, and 5 and
sub-harmonics Ns = 1/3 and 4, when superimposed and combined,
yield a group of curves with five areas of maximum deflection.
The areas of maximum deflection are at 10, 18, 25, 31, and 37 inch
( 25, 45,63, 77, and 93 cm), respectively, from the guide
sprocket 6.
~n alternative arrangement with similar damping is attained by
providing ten thru-slots with a diameter of 1.5 inch (4 cm)
( 10 slots of 1.5 inch diameter have about -the same surface area
of 5 holes of 2 inch diameter), each filled with a damping insert
and located in pairs in each of the five areas of maximum
deflection, i.e. at (8, 12), (16, 20), (23, 26), (29, 32), and
(35, 38) inch ( 20, 30, 41, 51, 58, 66, 74, 90 and 97 cm),
respectively, from guide sprocket 6 on -the longitudinal axis
of the chain bar.
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For chain bar d, i-t follows from Table III that the chain bar has !
resonant frequencies in the 100 to 400 Hertz range at 138 and 386
Hertz for n = 2 and 3 of the transverse harmonics, at 286 and 215
Hertz for Ns = 1/3 and 4 of the longitudinal sub-harmonics, and at
131 and 197 Hertz for n = 4 and 5, respectively, of the lateral
harmonics. It can be seen by comparison with the resonant
frequencies in the chain bar of chain saw c, that more damping
is required for the n = 3 transverse harmonics (higher resonant
frequency), but less for the n =4 and 5 lateral harmonics
(lower resonant frequencies). For chain saw d, the same number of
thru-slots with inser-ts wi-th the same diameter and locations ,
including the alternative arrangement as described above for
chain saw c7may be used.
.
Refe
1, Anon., Third International Symposium on Hand--Arm Vibrations,
Ottawa, 1981.
2. W. C. Leithl A Bar for a Power Chain Saw, Canada patent
1173330, 1984
3. R. N. Miles, Beam Dampers -for Damping the Vibrations of the
Skin of Reinforced Structures, ~SA patent 4425980, :L984.
4. W. Swallow, An Improved Method of Damping Panel Vibrations,
British patent 513171, 1939.
5. D. Ross et a]., Damping of Plate Flexural Vibrations by Means
of Viscoelastic Laminae, ASME Structural Damping
- Symposium, 1959.
6. W. C. Leith, A Cavitation Signature Indicates a Prevention
and a Cure for Vibration White Finger in Tree-Fallers,
ASME; Wood, Pulp and Forest Conference; Corvallis OR,
October 1983, separate volume.
7. J.P. den Hartog, Mechanical Vibrations,
; McGraw Hill, NY 1956
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